August 16, 2007

Game Theory

Posted in Nerdiness, The Why at 7:34 am by Dagny Taggart

Big doings today.  Too nervous to write something new, so you’re getting that Game Theory analysis I yammered about some time ago.  Less geeky topics when my hands have stopped shaking, I promise.

I took Game Theory for my Government major, and thus the class was skewed toward application in economic and international relations contexts.

At the time, I was also taking three classes for my English major ( British Victorian Novels, Shakespeare’s Histories and Comedies, and a seminar on Classic Lit.). I started thinking about the Prisoner’s Dilemma, and how it could apply to interpersonal relationships, and how maybe when people cooperate, they reach the interpersonal Nash equilibrium.

I am, in fact, the nerdiest chick anyone knows.  Seriously. I quote “Real Genius” like it’s my job, and now I’m talking Nash? Intervention?   Please?

So the Prisoner’s Dilemma involves incomplete information and decision-making, and can be applied to single-round or repeat interactions. Largely, each of two players can decide to trust, or not. If they both trust, they achieve the optimal outcome, or the end result with the highest “score” – as when two suspects charged with the same crime choose to trust each other and not confess. Both go to jail, but receive lighter sentences, because there is insufficient evidence to convict of greater charges, as denoted in the top left square.

If they both choose not to trust, they achieve the lowest possible “score” – that is, they both receive longer punishments, and thus have less benefit, as noted at the bottom right.

If either chooses not to trust when the other does, the trusting party is, essentially screwed – he/she gets zero benefit, while the other tra la las merrily along. Note, however, that this option still carries a larger total utility score than when neither party trusts.

 

Option A

Option B

Option A

25, 25

 

Total = 50

30, 0

 

Total = 30

Option B

0, 30

 

Total = 30

10, 10

 

Total = 20

So the point of all of this is that it is consistently more beneficial overall to extend trust.

But when you’ve extended trust in the past, and been screwed, it’s hard to do it.  However, if you’re anticipating repeated interactions with the same person, as in the dating/relationship context, it’s clearly worth it.  Once you’ve opted to “not cooperate”, the other person is motivated to be selfish as well, to protect his or her own interests.

Sometimes, it’s best just to walk away from the game entirely, if you think you’ll never get to the full cooperation box with the other party.  Sometimes, the important thing is to realize that you need to be okay with how you’re acting, regardless of whether the other person is being selfish or not.

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7 Comments »

  1. vvk said,

    Mmmm… mathy geeky goodness. 🙂

  2. Lisa said,

    Yah, once you’ve been screwed, it’s really hard – some might even venture impossible – to trust. Even if you know in your head it’s better for yourself and the world around you to have faith in others, the universe, love…

  3. vvk: Every so often, I manage to overcome my aversion to things mathematical by disguising them as sociology. Much like the melted-cheese-on-broccoli trick of yore. 😉

    Lisa: I think the key is believing that the optimal outcome can, in fact, be achieved. If you believe that, it makes another go-round of trusting something easier to stomach. Or it does for me, anyway. 🙂

  4. Trust issues? Like trusting other people or yourself? Technically it’s a moot point [in my eyes anyway]. It’s something that warrants discussion to be sure however…I just don’t get it.

    May have to discuss this offline I’m thinking…ehhh

  5. HBMS: GAAAAHHHH!!! I hate that phrase.

    I have issues trusting other people. And I have issues trusting myself to trust the right people. Which is more or less the same thing. 😕

  6. WiB said,

    Your mother puts license plates in your underwear?? How do you sit?

    One of the best movie lines ever. I will tolerate no argument on the matter.

  7. nullp0inter said,

    Are you quoting the real Nash or Sylvia Nasar’s “A Beautiful Mind” Nash, who is as handsome as a greek god?

    Two very different people. The movie was a mangling of his theory. “Adam Smith is wrong.”

    No shit! That’s not what Nash figured out though. He most proud of his manifold embeddings :-/


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